Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify812.0ms

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	296	15
6	532	15
7	1080	15
done	5001	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize8.0ms

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:

20.0ms	(* (- x y) (+ x y))
3.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (- x y) (+ x y))
29.0ms	(+ (* x x) (* y y))
59.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify723.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	127	1238
1	417	1187
2	2234	1033
done	5000	1033

prune188.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

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)))

rewrite38.0ms

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:

3.0ms	(+ (* x x) (* y y))
9.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
11.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series235.0ms

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))
73.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
59.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify908.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (183.0ms)

Iter	Nodes	Cost
0	158	2940
1	505	2546
2	2520	2246
done	5000	2246

prune297.0ms

Pruning

6 alts after pruning (5 fresh and 1 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)))

rewrite107.0ms

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:

20.0ms	(cbrt (pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3))
29.0ms	(pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3)
19.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
13.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3))
76.0ms	(pow (/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) 3)
63.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
67.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify569.0ms

Counts

379 → 379

Iterations

Useful iterations: done (555.0ms)

Iter	Nodes	Cost
0	436	12379
1	1428	10566
done	5000	9841

prune457.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (sqrt (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))))
16.4b	(sqrt (+ (* x x) (* y y)))
16.4b	(sqrt (+ (* x x) (* y y)))
16.5b	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

669×	`times-frac`
262×	`add-sqr-sqrt`
260×	`add-cube-cbrt` `*-un-lft-identity`
228×	`sqrt-prod`
83×	`associate-/r*`
55×	`associate-/r/`
54×	`sqrt-div`
43×	`add-exp-log`
30×	`flip3-+` `flip-+` `div-inv`
25×	`div-exp`
23×	`add-cbrt-cube`
11×	`cbrt-undiv`
8×	`associate-/l/`
7×	`pow1`
4×	`frac-times` `rec-exp` `1-exp` `prod-exp` `associate-/l*` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `clear-num` `cbrt-unprod`
1×	`pow-flip` `inv-pow`

Counts

4 → 407

Calls

4 calls:

34.0ms	(/ 1 (/ (sqrt (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
15.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (/ (sqrt (+ (* x x) (* y y))) (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))))
35.0ms	(sqrt (+ (* x x) (* y y)))
35.0ms	(sqrt (+ (* x x) (* y y)))
79.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify553.0ms

Counts

419 → 419

Iterations

Useful iterations: done (536.0ms)

Iter	Nodes	Cost
0	547	17399
1	1394	15740
done	5000	14050

prune680.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes81.0ms

Accuracy

76.9% (4.5b remaining)

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

bsearch107.0ms

Steps

Iters	Range	Point
9	6.482163761054332e-170	1.0769594822631765e-162	1.0639458246816258e-162
8	-1.9094341285360354e-159	-3.353351325512437e-163	-1.1106249786105219e-160
11	-3.485468065955809e+171	-4.6169799343652e+144	-1.4984271813117974e+147

Iters

Range

Point

6.482163761054332e-170

1.0769594822631765e-162

1.0639458246816258e-162

-1.9094341285360354e-159

-3.353351325512437e-163

-1.1106249786105219e-160

-3.485468065955809e+171

-4.6169799343652e+144

-1.4984271813117974e+147

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	56
1	34	37
done	34	37

end0.0ms

sample468.0ms

Algorithm

intervals

Results

228.0ms	8000×	body	80	valid
107.0ms	8000×	pre	80	true