Details

Time bar (total: 11.3s)

sample28.0ms

Algorithm
intervals
Results
12.0ms401×body80valid

simplify76.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
0815
11515
22513
3389
4489
5529
done529

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
6×sum-log
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+l+ *-un-lft-identity flip3-+ add-cbrt-cube flip-+
Counts
1 → 14
Calls
1 calls:
179.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series64.0ms

Counts
1 → 3
Calls
1 calls:
64.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify577.0ms

Counts
17 → 17
Iterations

Useful iterations: done (576.0ms)

IterNodesCost
041360
1144351
2794268
done5002251

prune53.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (+ (* x y) (* z (+ z z))) (* z z))) (cbrt (+ (+ (* x y) (* z (+ z z))) (* z z))))
2.5b
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))
2.5b
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))
2.5b
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
202.0ms
(* (cbrt (+ (+ (* x y) (* z (+ z z))) (* z z))) (cbrt (+ (+ (* x y) (* z (+ z z))) (* z z))))
17.0ms
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))
30.0ms
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))
18.0ms
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))

series943.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(* (cbrt (+ (+ (* x y) (* z (+ z z))) (* z z))) (cbrt (+ (+ (* x y) (* z (+ z z))) (* z z))))
233.0ms
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))
204.0ms
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))
211.0ms
(cbrt (+ (+ (* x y) (* z (+ z z))) (* z z)))

simplify1.3s

Counts
99 → 99
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01343224
13303035
211952517
done50002197

prune603.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (+ (* x y) (* 2 (pow z 2))) (* z z))
0.3b
(* (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))) (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))))
2.0b
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))
2.0b
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ add-log-exp
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down sum-log pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 associate-+l+ pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 100
Calls
4 calls:
58.0ms
(+ (+ (* x y) (* 2 (pow z 2))) (* z z))
208.0ms
(* (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))) (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))))
48.0ms
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))
61.0ms
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (+ (* x y) (* 2 (pow z 2))) (* z z))
57.0ms
(* (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))) (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))))
151.0ms
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))
180.0ms
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))

simplify1.1s

Counts
112 → 112
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01023289
12502420
212651772
done50021733

prune472.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))) (* (fabs (cbrt (+ (* 3 (* z z)) (* x y)))) (sqrt (cbrt (+ (* 3 (* z z)) (* x y))))))
2.0b
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))
2.5b
(cbrt (+ (* 3 (* z z)) (* x y)))
2.5b
(cbrt (+ (* 3 (* z z)) (* x y)))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-div
10×pow1 add-sqr-sqrt cbrt-div
9×add-exp-log add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
8×associate-*r/
6×cbrt-prod associate-*l* sqrt-prod
4×frac-times add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×pow1/3 associate-*l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 70
Calls
4 calls:
222.0ms
(* (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))) (* (fabs (cbrt (+ (* 3 (* z z)) (* x y)))) (sqrt (cbrt (+ (* 3 (* z z)) (* x y))))))
74.0ms
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))
27.0ms
(cbrt (+ (* 3 (* z z)) (* x y)))
28.0ms
(cbrt (+ (* 3 (* z z)) (* x y)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(* (sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z))) (* (fabs (cbrt (+ (* 3 (* z z)) (* x y)))) (sqrt (cbrt (+ (* 3 (* z z)) (* x y))))))
164.0ms
(sqrt (+ (+ (* x y) (* 2 (pow z 2))) (* z z)))
169.0ms
(cbrt (+ (* 3 (* z z)) (* x y)))
178.0ms
(cbrt (+ (* 3 (* z z)) (* x y)))

simplify1.0s

Counts
82 → 82
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01902704
15052516
217482065
done50011984

prune501.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes510.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11215
done1215

end0.0ms

sample1.5s

Algorithm
intervals
Results
866.0ms12315×body80valid