Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	47	15
3	86	15
4	166	15
5	291	15
6	520	15
7	869	15
8	2673	15
done	5000	15

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
16.7b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

16.0ms	(* (- x y) (+ x y))
2.0ms	(+ (* x x) (* y y))
16.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series129.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (- x y) (+ x y))
26.0ms	(+ (* x x) (* y y))
63.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify793.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (241.0ms)

Iter	Nodes	Cost
0	127	1238
1	411	1187
2	1945	1033
done	5000	1033

prune177.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
0.0b	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
16.7b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`unpow-prod-down` `cube-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `times-frac` `add-cbrt-cube`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`pow-unpow` `flip3--` `pow-exp` `associate-/r*` `flip--` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

2.0ms	(+ (* x x) (* y y))
6.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
10.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
77.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
72.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
62.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify729.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (261.0ms)

Iter	Nodes	Cost
0	158	2940
1	484	2546
2	2106	2246
done	5000	2246

prune270.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3))
0.0b	(pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3)
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
16.7b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
141×	`associate-/r/`
120×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
106×	`cbrt-prod`
100×	`unpow-prod-down` `cube-prod`
68×	`frac-times`
52×	`add-exp-log` `flip3-+` `flip-+`
51×	`flip3--` `flip--`
34×	`associate-r/` `associate-l/`
28×	`add-cbrt-cube`
26×	`div-exp`
22×	`div-inv`
16×	`associate-/r*`
12×	`cbrt-undiv`
10×	`pow-exp`
7×	`pow1` `prod-exp`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`add-log-exp` `rem-cube-cbrt`
3×	`pow-unpow` `pow-pow` `cbrt-unprod`
2×	`cube-div` `cube-mult` `pow-flip` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `inv-pow` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow1/3` `rem-cbrt-cube`

Counts

4 → 367

Calls

4 calls:

19.0ms	(cbrt (pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3))
25.0ms	(pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3)
18.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
16.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(cbrt (pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3))
69.0ms	(pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3)
55.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
60.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify1.3s

Counts

379 → 379

Iterations

Useful iterations: 2 (653.0ms)

Iter	Nodes	Cost
0	436	12379
1	1267	10540
2	3702	9473
done	5001	9473

prune427.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y)))
0.2b	(* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y))
16.5b	(/ (+ (* x x) (* y y)) (- x y))
16.6b	(/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
99×	`add-exp-log`
78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
61×	`add-cbrt-cube`
45×	`add-cube-cbrt`
43×	`div-exp`
33×	`associate-l`
30×	`prod-exp`
29×	`associate-/r/`
27×	`associate-/l*`
25×	`cbrt-undiv`
17×	`flip3-+` `flip-+`
16×	`cbrt-unprod`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`frac-times`
9×	`pow1`
8×	`associate-*r/`
7×	`associate-/r*` `div-inv`
6×	`rec-exp` `1-exp` `associate-*l/`
4×	`flip3--` `associate-r` `flip--` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/` `unswap-sqr`
2×	`pow-flip` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `distribute-lft-out` `inv-pow`

Counts

4 → 224

Calls

4 calls:

60.0ms	(/ 1 (* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y)))
60.0ms	(* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y))
11.0ms	(/ (+ (* x x) (* y y)) (- x y))
22.0ms	(/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1 (* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y)))
58.0ms	(* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y))
57.0ms	(/ (+ (* x x) (* y y)) (- x y))
61.0ms	(/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y)))

simplify1.5s

Counts

236 → 236

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	301	6091
1	1034	5886
2	3628	4434
done	5000	4361

prune560.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes79.0ms

Accuracy

77.2% (4.4b remaining)

Error of 4.9b against oracle of 0.4b and baseline of 19.9b

bsearch97.0ms

Steps

Iters	Range	Point
9	6.482163761054332e-170	1.0769594822631765e-162	1.0639458246816258e-162
7	-3.353351325512437e-163	-1.948959072094272e-164	-3.3090200342718626e-163
8	-6.820128030937311e+65	-2.817955795644209e+61	-1.2621726567179237e+64

Iters

Range

Point

6.482163761054332e-170

1.0769594822631765e-162

1.0639458246816258e-162

-3.353351325512437e-163

-1.948959072094272e-164

-3.3090200342718626e-163

-6.820128030937311e+65

-2.817955795644209e+61

-1.2621726567179237e+64

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	76
1	38	49
done	38	49

end0.0ms

sample477.0ms

Algorithm

intervals

Results

235.0ms	8000×	body	80	valid
106.0ms	8000×	pre	80	true