Details

sample61.0ms

Algorithm

intervals

Results

28.0ms

258×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1945
3	460
2	138
1	55
0	29

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
22.1b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

33.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
21.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
77.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
181.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series512.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
88.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
90.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
269.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify2.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	4284
1	689
0	226

prune884.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
20.8b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

46.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
25.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
67.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
103.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series538.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
85.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
102.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
291.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify2.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5002
2	3046
1	577
0	211

prune862.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.3b	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
20.8b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
110×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
74×	`add-cube-cbrt`
18×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
10×	`flip3-+` `flip-+`
8×	`pow1` `div-inv` `associate-/l*`
6×	`associate-r` `associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 184

Calls

4 calls:

20.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
103.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
122.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
132.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series660.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
76.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
332.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
182.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.1s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
1	1063
0	348

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)
17.2b	(/ (- (pow x 3) (pow 2.0 3)) (/ (+ 47.066876606 (* x (+ 313.399215894 (* (+ (* x (+ 43.3400022514 x)) 263.505074721) x)))) (/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0))))))
17.8b	(/ (+ 47.066876606 (* x (+ 313.399215894 (* (+ (* x (+ 43.3400022514 x)) 263.505074721) x)))) (/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0)))))
18.3b	(/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0))))

rewrite590.0ms

Algorithm

rewrite-expression-head

Rules

3212×	`times-frac`
2297×	`add-sqr-sqrt`
1581×	`*-un-lft-identity`
1071×	`add-cube-cbrt`
816×	`difference-of-squares`
612×	`unpow-prod-down` `cube-prod`
408×	`sqr-pow`
255×	`distribute-lft-out--`
194×	`associate-/r/`
111×	`div-inv`
86×	`flip3-+` `flip-+`
68×	`associate-/r*`
51×	`difference-cubes`
31×	`associate-/l*`
22×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
6×	`pow1` `associate-/l/`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l`
2×	`associate-*l/`
1×	`flip3--` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 1476

Calls

4 calls:

90.0ms	(* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)
164.0ms	(/ (- (pow x 3) (pow 2.0 3)) (/ (+ 47.066876606 (* x (+ 313.399215894 (* (+ (* x (+ 43.3400022514 x)) 263.505074721) x)))) (/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0))))))
63.0ms	(/ (+ 47.066876606 (* x (+ 313.399215894 (* (+ (* x (+ 43.3400022514 x)) 263.505074721) x)))) (/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0)))))
58.0ms	(/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)
429.0ms	(/ (- (pow x 3) (pow 2.0 3)) (/ (+ 47.066876606 (* x (+ 313.399215894 (* (+ (* x (+ 43.3400022514 x)) 263.505074721) x)))) (/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0))))))
226.0ms	(/ (+ 47.066876606 (* x (+ 313.399215894 (* (+ (* x (+ 43.3400022514 x)) 263.505074721) x)))) (/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0)))))
341.0ms	(/ (+ z (* (+ (* x (+ (* (+ (* 4.16438922228 x) 78.6994924154) x) 137.519416416)) y) x)) (+ (* x x) (* 2.0 (+ x 2.0))))

simplify5.2s

Counts

1488 → 1488

Iterations

Iter	Nodes
done	5000
0	1718

prune13.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes436.0ms

Accuracy

95.2% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 25.3b

bsearch349.0ms

Steps

Iters	Range		Point
9	488997712.5877659	631776370996477.2	620615997107907.6
3	-6.376815652518718e+28	-5.267362834597857e+28	-6.307474851398664e+28

simplify47.0ms

Iterations

Iter	Nodes
done	78
3	78
2	76
1	73
0	50

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

8010×

body

valid