Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	20
1	13
0	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`add-sqr-sqrt`
4×	`pow1` `sum-log` `*-un-lft-identity` `add-cube-cbrt`
3×	`flip3-+` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `flip-+`
2×	`+-commutative` `sqrt-div`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

3 → 39

Calls

3 calls:

6.0ms	(+ (* x x) (* y y))
40.0ms	(+ (+ (* x x) (* y y)) (* z z))
47.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* x x) (* y y))
62.0ms	(+ (+ (* x x) (* y y)) (* z z))
156.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify663.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1317
1	236
0	74

prune287.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.2b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune10.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 18.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y))) (* z z))
8.8b	(- (pow x 4) (pow y 4))
35.2b	(sqrt (+ (/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y))) (* z z)))
40.8b	(/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y)))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
27×	`difference-of-squares`
24×	`unpow-prod-down`
19×	`*-un-lft-identity`
18×	`sqr-pow`
14×	`times-frac` `associate-/l*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/` `add-log-exp`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--`
5×	`pow1` `flip3-+` `flip3--` `flip-+` `flip--`
4×	`frac-times`
3×	`sqrt-prod`
2×	`cbrt-undiv` `sqrt-div` `div-sub` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `prod-exp` `associate-+l-` `cbrt-unprod` `div-inv`

Counts

4 → 104

Calls

4 calls:

132.0ms	(+ (/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y))) (* z z))
29.0ms	(- (pow x 4) (pow y 4))
183.0ms	(sqrt (+ (/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y))) (* z z)))
95.0ms	(/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ (/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y))) (* z z))
68.0ms	(- (pow x 4) (pow y 4))
260.0ms	(sqrt (+ (/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y))) (* z z)))
112.0ms	(/ (- (pow x 4) (pow y 4)) (* (+ x y) (- x y)))

simplify1.2s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	2538
1	516
0	198

prune700.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 18.2b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 18.2b

regimes808.0ms

Accuracy

50.7% (9.7b remaining)

Error of 28.1b against oracle of 18.5b and baseline of 38.1b

bsearch247.0ms

Steps

Iters	Range		Point
10	2.1840898211063394e+107	4.907435983426589e+125	6.610853035061559e+124
9	4.5529622625386965e-164	4.557376285322506e-157	5.893708537160268e-164
8	-9.251454744754915e-293	-2.5719590943528753e-297	-2.7078218728103666e-297
9	-3.460397846028137e+74	-2.112574128781726e+65	-3.3929769808570974e+74

simplify5.0ms

Iterations

Iter	Nodes
done	24
1	24
0	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

704.0ms

8000×

body

valid