Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	22	14
3	25	14
done	25	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

47.0ms	(+ (+ (* x x) (* y y)) (* z z))
92.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
54.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series357.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (+ (* x x) (* y y)) (* z z))
71.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
238.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify839.0ms

Counts

76 → 76

Iterations

Useful iterations: done (835.0ms)

Iter	Nodes	Cost
0	123	1541
1	283	1474
2	1246	1348
done	5002	1346

prune299.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (pow y 2) (pow z 2)))
0.0b	(+ (pow y 2) (pow z 2))
0.1b	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
37.9b	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
12×	`distribute-lft-out`
11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt` `unpow-prod-down`
6×	`add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube`
4×	`flip3-+` `associate-*r/` `sum-log` `flip-+`
3×	`associate-l`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

66.0ms	(+ (pow x 2) (+ (pow y 2) (pow z 2)))
27.0ms	(+ (pow y 2) (pow z 2))
231.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
71.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (pow x 2) (+ (pow y 2) (pow z 2)))
43.0ms	(+ (pow y 2) (pow z 2))
87.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
221.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify838.0ms

Counts

79 → 79

Iterations

Useful iterations: done (835.0ms)

Iter	Nodes	Cost
0	101	1216
1	294	1108
2	1509	1024
done	5002	1016

prune284.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
0.1b	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
37.8b	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

48.0ms	(+ (+ (* x x) (* y y)) (* z z))
99.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
123.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
75.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

series930.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (+ (* x x) (* y y)) (* z z))
260.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
160.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
456.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

simplify1.4s

Counts

181 → 181

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	269	5521
1	581	5180
2	2959	4752
done	5000	4636

prune675.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
37.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.8b	(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0)) (/ (pow (cbrt 3.0) 2) (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

8297×	`times-frac`
5575×	`sqrt-prod`
3662×	`add-sqr-sqrt`
3475×	`add-cube-cbrt` `*-un-lft-identity`
2069×	`cbrt-prod`
1460×	`unpow-prod-down`
250×	`unpow2` `sqr-pow`
114×	`div-inv`
87×	`sqrt-div`
81×	`associate-/r/`
58×	`rem-sqrt-square`
43×	`flip3-+` `flip-+`
7×	`pow1`
6×	`add-exp-log` `associate-/r` `associate-/l`
5×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 3043

Calls

4 calls:

60.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
481.0ms	(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0)) (/ (pow (cbrt 3.0) 2) (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series929.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
126.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
122.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
368.0ms	(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0)) (/ (pow (cbrt 3.0) 2) (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify2.0s

Counts

3055 → 3055

Iterations

Useful iterations: 0 (457.0ms)

Iter	Nodes	Cost
0	5753	222526
done	5753	222526

prune18.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.9b

regimes380.0ms

Accuracy

57.5% (8.2b remaining)

Error of 27.0b against oracle of 18.7b and baseline of 38.1b

bsearch162.0ms

Steps

Iters	Range		Point
8	1.9445145714521144e+92	6.598426988503463e+95	2.9682675892586475e+95
7	6.123354719305387e-149	4.8857590053090926e-147	6.220903762266977e-149
9	8.975843869006682e-209	1.807242467643983e-199	5.393455774424304e-203
8	-1.6504271973040736e+100	-3.113286269135709e+96	-1.629188860154807e+100

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	64
1	50	64
2	52	64
done	52	64

end0.0ms

sample974.0ms

Algorithm

intervals

Results

625.0ms

8000×

body

valid