Details

Time bar (total: 7.0s)

sample28.0ms

Algorithm
intervals
Results
12.0ms269×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11515
done1515

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.3b

Counts
2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(+ (* a c) (* b d))
27.8b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
4.0ms
(+ (* c c) (* d d))
4.0ms
(+ (* a c) (* b d))
9.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series44.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* c c) (* d d))
11.0ms
(+ (* a c) (* b d))
28.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.5s

Counts
62 → 62
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
0981090
12701067
2932951
33225951
done5001951

prune123.0ms

Filtered
50 candidates to 62 candidates (-24.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New521062
Fresh000
Picked101
Done000
Total531063

Merged error: 27.5b

Counts
63 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* a c) (* b d))
17.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.3b
(sqrt (+ (* c c) (* d d)))
29.3b
(sqrt (+ (* c c) (* d d)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
4.0ms
(+ (* a c) (* b d))
10.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(+ (* a c) (* b d))
38.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.3s

Counts
96 → 96
Iterations

Useful iterations: 3 (387.0ms)

IterNodesCost
01161780
12741649
27511541
320241525
done50011525

prune131.0ms

Filtered
75 candidates to 96 candidates (-28.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New93396
Fresh279
Picked101
Done000
Total9610106

Merged error: 23.8b

Counts
106 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* a c) (* b d))
17.9b
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.3b
(sqrt (+ (* c c) (* d d)))
29.3b
(sqrt (+ (* c c) (* d d)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
4.0ms
(+ (* a c) (* b d))
10.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* a c) (* b d))
37.0ms
(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.3s

Counts
96 → 96
Iterations

Useful iterations: 3 (390.0ms)

IterNodesCost
01161780
12741649
27511541
320241525
done50011525

prune128.0ms

Filtered
75 candidates to 96 candidates (-28.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New96096
Fresh099
Picked011
Done000
Total9610106

Merged error: 23.8b

Counts
106 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* c c) (pow d 2))
0.5b
(+ (* a c) (* d b))
1.0b
(/ 1 (/ (+ (* c c) (pow d 2)) (+ (* a c) (* d b))))
27.1b
(/ (+ (* c c) (pow d 2)) (+ (* a c) (* d b)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ add-log-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
5.0ms
(+ (* c c) (pow d 2))
4.0ms
(+ (* a c) (* d b))
12.0ms
(/ 1 (/ (+ (* c c) (pow d 2)) (+ (* a c) (* d b))))
11.0ms
(/ (+ (* c c) (pow d 2)) (+ (* a c) (* d b)))

series67.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* c c) (pow d 2))
10.0ms
(+ (* a c) (* d b))
31.0ms
(/ 1 (/ (+ (* c c) (pow d 2)) (+ (* a c) (* d b))))
19.0ms
(/ (+ (* c c) (pow d 2)) (+ (* a c) (* d b)))

simplify733.0ms

Counts
149 → 149
Iterations

Useful iterations: done (728.0ms)

IterNodesCost
02033676
15063418
214183113
done50013111

prune169.0ms

Filtered
89 candidates to 149 candidates (-67.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1481149
Fresh178
Picked011
Done011
Total14910159

Merged error: 23.8b

Counts
159 → 10

regimes456.0ms

Accuracy

40.8% (1.9b remaining)

Error of 25.6b against oracle of 23.7b and baseline of 27.0b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02483
13183
done3183

end0.0ms

sample801.0ms

Algorithm
intervals
Results
396.0ms8479×body80valid

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