Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify4.5s

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
19.8b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite142.0ms

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:

73.0ms	(* (- x y) (+ x y))
17.0ms	(+ (* x x) (* y y))
49.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* (- x y) (+ x y))
55.0ms	(+ (* x x) (* y y))
100.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	127	1238
1	406	1187
2	1986	1037
done	5000	1026

prune233.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

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)
19.8b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite119.0ms

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:

18.0ms	(+ (* x x) (* y y))
30.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
31.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
32.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* x x) (* y y))
111.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
113.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
103.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.5s

Counts

128 → 128

Iterations

Useful iterations: 2 (511.0ms)

Iter	Nodes	Cost
0	158	2940
1	486	2546
2	2131	2246
done	5000	2246

prune409.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

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)
0.2b	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
19.2b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log` `add-cbrt-cube`
10×	`cube-div`
9×	`pow1`
8×	`cbrt-prod`
7×	`distribute-lft-out`
6×	`frac-times` `flip3--` `associate-*l/` `flip--`
5×	`cbrt-div` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `flip3-+` `associate-r/` `div-exp` `pow-exp` `associate-/r` `flip-+` `rem-cube-cbrt`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `div-inv` `associate-/l/` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/3` `clear-num` `*-commutative` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

5.0ms	(cbrt (pow (* (- x y) (/ (+ x y) (+ (* x x) (* y y)))) 3))
33.0ms	(pow (* (- x y) (/ (+ x y) (+ (* x x) (* y y)))) 3)
95.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
45.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (pow (* (- x y) (/ (+ x y) (+ (* x x) (* y y)))) 3))
94.0ms	(pow (* (- x y) (/ (+ x y) (+ (* x x) (* y y)))) 3)
83.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
56.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify1.6s

Counts

141 → 141

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	180	2748
1	473	2398
2	2312	2282
done	5000	2280

prune469.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (* (- x y) x) (* (- x y) y))
0.0b	(* (- x y) y)
19.8b	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

9.0ms	(+ (* x x) (* y y))
20.0ms	(+ (* (- x y) x) (* (- x y) y))
25.0ms	(* (- x y) y)
62.0ms	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
50.0ms	(+ (* (- x y) x) (* (- x y) y))
55.0ms	(* (- x y) y)
71.0ms	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	160	1922
1	454	1616
2	1778	1472
done	5001	1456

prune289.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes169.0ms

Accuracy

77.5% (4.5b remaining)

Error of 5.0b against oracle of 0.4b and baseline of 20.6b

bsearch126.0ms

Steps

Iters	Range	Point
6	7.57387563408003e-178	3.856205723104632e-177	3.81890050297606e-177
8	-7.653706237395124e-160	-1.7669547785881474e-162	-8.743307936790759e-162
10	-4.868209042395978e+158	-1.1489753180495791e+148	-5.3752784922532734e+150

Iters

Range

Point

7.57387563408003e-178

3.856205723104632e-177

3.81890050297606e-177

-7.653706237395124e-160

-1.7669547785881474e-162

-8.743307936790759e-162

-4.868209042395978e+158

-1.1489753180495791e+148

-5.3752784922532734e+150

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	52
1	36	52
done	36	52

end0.0ms

sample949.0ms

Algorithm

intervals

Results

417.0ms	8000×	body	80	valid
266.0ms	8000×	pre	80	true