Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	48	15
3	101	15
4	188	15
5	346	15
6	579	15
7	875	15
8	2271	15
done	5000	15

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

17.0ms	(+ (* x x) (* y y))
48.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* x x) (* y y))
89.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify895.0ms

Counts

48 → 48

Iterations

Useful iterations: done (893.0ms)

Iter	Nodes	Cost
0	91	826
1	303	802
2	1443	662
done	5000	655

prune158.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (pow y 2))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

23.0ms	(+ (* x x) (pow y 2))
68.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

series135.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x x) (pow y 2))
102.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

simplify928.0ms

Counts

48 → 48

Iterations

Useful iterations: done (926.0ms)

Iter	Nodes	Cost
0	91	826
1	296	794
2	1358	666
done	5001	661

prune162.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2))))
0.0b	(+ (* x x) (pow y 2))
0.0b	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

18×	`exp-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`log-pow`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-/l/`
7×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`frac-times`
3×	`log-prod` `flip3--` `associate-/r*` `flip--` `div-inv`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`+-commutative` `frac-2neg` `rem-log-exp` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `rem-exp-log` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

75.0ms	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2))))
21.0ms	(+ (* x x) (pow y 2))
69.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))))
43.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2))))
49.0ms	(+ (* x x) (pow y 2))
111.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))))
83.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

simplify770.0ms

Counts

92 → 92

Iterations

Useful iterations: done (767.0ms)

Iter	Nodes	Cost
0	129	1610
1	342	1519
2	1438	1302
done	5001	1293

prune358.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2))))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/l/`
19×	`add-exp-log` `add-cbrt-cube`
13×	`flip3-+` `flip-+`
12×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`cbrt-prod` `flip3--` `associate-/r*` `flip--`
8×	`associate-/r/`
6×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`cbrt-div` `pow1/3`

Counts

4 → 111

Calls

4 calls:

29.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2))))
44.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))
58.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))
49.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2))))
96.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))
94.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))
81.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

simplify1.1s

Counts

123 → 123

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	110	2452
1	315	2370
2	1383	2030
done	5000	2014

prune587.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes78.0ms

Accuracy

75.7% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 19.9b

bsearch104.0ms

Steps

Iters	Range		Point
9	9.133840493531702e-163	9.628535965427897e-156	7.168109854324842e-160
9	-1.1690025963777955e-148	-8.983747944314465e-154	-1.1129546130770477e-151
7	-108.09236434424712	-0.7718806003288846	-106.30606884619185

simplify5.0ms

Iterations

Useful iterations: done (5.0ms)

Iter	Nodes	Cost
0	27	50
1	33	49
done	33	48

end0.0ms

sample1.1s

Algorithm

intervals

Results

553.0ms	8000×	body	80	valid
240.0ms	8000×	pre	80	true