Details

Time bar (total: 20.6s)

sample50.0ms

Algorithm
intervals
Results
27.0ms256×body80valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×sum-log
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 78
Calls
4 calls:
8.0ms
(+ (* x x) (* y y))
41.0ms
(+ (+ (* x x) (* y y)) (* z z))
152.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
60.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series405.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (* x x) (* y y))
41.0ms
(+ (+ (* x x) (* y y)) (* z z))
67.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
253.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.0s

Counts
90 → 90
Iterations

Useful iterations: 3 (945.0ms)

IterNodesCost
01391707
13191620
29481477
332451461
done50001461

prune428.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
34.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.1b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 106
Calls
4 calls:
88.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
37.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
40.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
91.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
319.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
141.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
151.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
467.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify3.2s

Counts
118 → 118
Iterations

Useful iterations: 3 (411.0ms)

IterNodesCost
01452892
12502456
25622347
314582289
444722289
done50012289

prune525.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.2b

localize35.0ms

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))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
34.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite414.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1 add-log-exp
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down sum-log associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times associate-+l+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
110.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
181.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
77.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
54.0ms
(+ (+ (* x x) (* y y)) (* z z))
189.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
466.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
438.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify2.8s

Counts
169 → 169
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02234498
14264299
211804070
339264054
done50004032

prune688.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
1.0b
(/ 1 (cbrt 3.0))
34.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite421.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
51×sqrt-prod
47×times-frac
43×*-un-lft-identity
39×add-cube-cbrt
29×sqrt-div
26×associate-*r*
25×cbrt-prod
18×pow1
16×associate-*l*
15×add-exp-log
12×add-cbrt-cube unswap-sqr
11×frac-times
10×pow-prod-down
8×associate-*r/
7×flip3-+ associate-*l/ flip-+
6×sqrt-pow1 pow1/2 associate-/r*
4×prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod div-inv associate-/l*
2×pow-flip div-exp *-commutative
1×cbrt-undiv rem-sqrt-square rec-exp frac-2neg pow1/3 1-exp clear-num inv-pow
Counts
4 → 160
Calls
4 calls:
99.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
253.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
11.0ms
(/ 1 (cbrt 3.0))
51.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series1.1s

Counts
4 → 10
Calls
4 calls:
567.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
401.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
0.0ms
(/ 1 (cbrt 3.0))
118.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.6s

Counts
170 → 170
Iterations

Useful iterations: done (3.5s)

IterNodesCost
02303710
14553312
211393090
343952960
done50002942

prune639.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.2b

regimes548.0ms

Accuracy

62.4% (7.5b remaining)

Error of 25.7b against oracle of 18.2b and baseline of 38.2b

bsearch115.0ms

Steps
ItersRangePoint
8
9.20494146023971e+137
7.045427827826125e+140
2.3365707403123e+138
6
-1.5895300252882697e+103
-1.0869981655899858e+102
-1.5627024897583575e+103

simplify13.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03364
14564
24764
done4764

end0.0ms

sample872.0ms

Algorithm
intervals
Results
557.0ms8000×body80valid