Details

sample301.0ms

Algorithm

intervals

Results

140.0ms	1400×	body	80	nan
33.0ms	412×	body	80	valid
5.0ms	12×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	1×	body	1280	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (67.0ms)

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize36.0ms

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))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0b	(log (- 1.0 z))

rewrite172.0ms

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:

68.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
55.0ms	(* y (- (log z) t))
40.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

series714.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
138.0ms	(* y (- (log z) t))
289.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
55.0ms	(log (- 1.0 z))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: done (1.1s)

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

prune670.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

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

rewrite1.7s

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:

1.0s	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
308.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
54.0ms	(* y (- (log z) t))
267.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series927.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
281.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
135.0ms	(* y (- (log z) t))
388.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify1.2s

Counts

135 → 135

Iterations

Useful iterations: done (1.2s)

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

prune894.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (* (/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z))))))) (pow z y)))
0.2b	(* (/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z))))))) (pow z y))
0.4b	(+ (* a b) (+ (* t y) (* 1.0 (* a z))))
7.9b	(* a (pow z 2))

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
57×	`add-exp-log`
40×	`prod-exp`
38×	`associate-l`
37×	`times-frac`
26×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
20×	`add-cbrt-cube`
18×	`div-exp`
16×	`associate-r` `unswap-sqr`
15×	`pow-to-exp` `pow-exp`
14×	`sqr-pow`
9×	`add-log-exp`
8×	`cbrt-unprod`
7×	`exp-sum`
6×	`pow1`
3×	`sum-log` `*-commutative`
2×	`cbrt-undiv` `associate-*l/` `unpow2`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `pow-prod-down` `flip-+` `div-inv`

Counts

4 → 144

Calls

4 calls:

2.6s	(* x (* (/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z))))))) (pow z y)))
1.2s	(* (/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z))))))) (pow z y))
43.0ms	(+ (* a b) (+ (* t y) (* 1.0 (* a z))))
13.0ms	(* a (pow z 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

610.0ms	(* x (* (/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z))))))) (pow z y)))
396.0ms	(* (/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z))))))) (pow z y))
76.0ms	(+ (* a b) (+ (* t y) (* 1.0 (* a z))))
43.0ms	(* a (pow z 2))

simplify1.6s

Counts

156 → 156

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	284	5279
1	736	5202
2	2660	4646
done	5001	4625

prune974.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
7.9b	(* a (pow z 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-r`
6×	`add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `add-log-exp` `unswap-sqr`
3×	`pow1/3` `associate-l` `prod-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
26.0ms	(* a (pow z 2))

series917.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt x)
296.0ms	(cbrt x)
306.0ms	(cbrt x)
51.0ms	(* a (pow z 2))

simplify4.3s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	74	427
1	145	392
2	311	341
3	832	332
4	3823	329
done	5001	329

prune530.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes480.0ms

Accuracy

72.6% (3.4b remaining)

Error of 3.4b against oracle of 0.0b and baseline of 12.3b

bsearch631.0ms

Steps

Iters	Range		Point
10	2.499699576950359e+119	6.816916420323158e+131	8.989039952438387e+120
8	-1204.6599638446712	-0.534938775438677	-1.436503598316957

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

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

end0.0ms

sample12.9s

Algorithm

intervals

Results

6.1s	41080×	body	80	nan
2.3s	12508×	body	80	valid
312.0ms	365×	body	640	valid
132.0ms	391×	body	320	valid
109.0ms	277×	body	160	valid
79.0ms	74×	body	1280	valid