Details

Time bar (total: 16.4s)

sample48.0ms

Algorithm
intervals
Results
21.0ms256×body80valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
done25
325
222
115
011

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×sqrt-prod
11×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1
4×sum-log
3×associate-/r* flip3-+ flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
4 → 78
Calls
4 calls:
48.0ms
(+ (+ (* x x) (* y y)) (* z z))
13.0ms
(+ (* x x) (* y y))
93.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series385.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (+ (* x x) (* y y)) (* z z))
37.0ms
(+ (* x x) (* y y))
68.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
229.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify743.0ms

Counts
90 → 90
Iterations
IterNodes
done5000
21770
1358
0139

prune709.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (/ (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) 3.0))
36.1b
(sqrt (+ (* z z) (+ (pow y 2) (* x x))))
36.1b
(sqrt (+ (* z z) (+ (pow y 2) (* x x))))
36.1b
(sqrt (* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (/ (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) 3.0)))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×*-un-lft-identity add-cube-cbrt
17×sqrt-div
11×pow1
9×add-cbrt-cube add-exp-log
6×flip3-+ associate-*l* flip-+ unswap-sqr
4×frac-times sqrt-pow1 associate-*l/ add-log-exp
3×pow1/2
2×rem-sqrt-square pow-prod-down prod-exp associate-*r/ cbrt-unprod
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
223.0ms
(* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (/ (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) 3.0))
61.0ms
(sqrt (+ (* z z) (+ (pow y 2) (* x x))))
41.0ms
(sqrt (+ (* z z) (+ (pow y 2) (* x x))))
90.0ms
(sqrt (* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (/ (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) 3.0)))

series569.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (/ (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) 3.0))
121.0ms
(sqrt (+ (* z z) (+ (pow y 2) (* x x))))
151.0ms
(sqrt (+ (* z z) (+ (pow y 2) (* x x))))
214.0ms
(sqrt (* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (/ (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) 3.0)))

simplify2.3s

Counts
110 → 110
Iterations
IterNodes
done5000
22816
1368
0141

prune852.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow y 2) (* x x))
0.1b
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0)))
0.1b
(/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0))
36.1b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0))))

rewrite404.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
51×times-frac add-exp-log
37×*-un-lft-identity
34×add-cube-cbrt
24×cbrt-prod
22×associate-*r*
20×prod-exp
19×add-cbrt-cube
16×div-exp
9×pow1 unswap-sqr
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×associate-/r* add-log-exp
4×rec-exp 1-exp
3×sqrt-div div-inv associate-/l*
2×frac-times sqrt-pow1 flip3-+ pow-prod-down associate-*l/ associate-*r/ flip-+ associate-/l/
1×+-commutative clear-num sum-log frac-2neg pow1/2 *-commutative sqrt-prod
Counts
4 → 136
Calls
4 calls:
20.0ms
(+ (pow y 2) (* x x))
182.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0)))
99.0ms
(/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0))
92.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0))))

series927.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (pow y 2) (* x x))
205.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0)))
199.0ms
(/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0))
465.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (* z z) (+ (pow y 2) (* x x))) (cbrt 3.0))))

simplify2.1s

Counts
148 → 148
Iterations
IterNodes
done5000
24972
1722
0227

prune969.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.8b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (cbrt 3.0))
36.1b
(sqrt (+ (+ (* x x) (* z z)) (pow y 2)))
36.1b
(sqrt (+ (+ (* x x) (* z z)) (pow y 2)))
36.1b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (/ (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (cbrt 3.0)))))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
42×times-frac
38×add-sqr-sqrt
37×sqrt-prod
36×add-cube-cbrt
25×sqrt-div
24×cbrt-prod
12×pow1
9×frac-times distribute-lft-out
7×flip3-+ associate-*r/ flip-+ associate-/l*
6×associate-/r* add-exp-log
5×sqrt-pow1 add-cbrt-cube associate-*l/
4×add-log-exp
3×pow1/2 pow-prod-down
2×rem-sqrt-square associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 124
Calls
4 calls:
72.0ms
(/ (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (cbrt 3.0))
38.0ms
(sqrt (+ (+ (* x x) (* z z)) (pow y 2)))
47.0ms
(sqrt (+ (+ (* x x) (* z z)) (pow y 2)))
223.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (/ (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (cbrt 3.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
330.0ms
(/ (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (cbrt 3.0))
119.0ms
(sqrt (+ (+ (* x x) (* z z)) (pow y 2)))
150.0ms
(sqrt (+ (+ (* x x) (* z z)) (pow y 2)))
433.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (/ (sqrt (+ (+ (* x x) (* z z)) (pow y 2))) (cbrt 3.0)))))

simplify1.0s

Counts
136 → 136
Iterations
IterNodes
done5000
21146
1338
0182

prune973.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.0b

regimes1.0s

Accuracy

37% (19.2b remaining)

Error of 25.9b against oracle of 6.7b and baseline of 37.2b

bsearch120.0ms

Steps
ItersRangePoint
9
1.5958334848383986e+119
1.6343128467780486e+124
7.898403675517638e+123
9
-7.123290046831777e+50
-4.989343308395731e+45
-7.0606062487436015e+50

simplify6.0ms

Iterations
IterNodes
done30
230
127
022

end0.0ms

sample916.0ms

Algorithm
intervals
Results
559.0ms8000×body80valid