Details

Time bar (total: 5.2s)

sample29.0ms

Algorithm
intervals
Results
13.0ms267×body80valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.9b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
1.0b
(- (* b c) (* a d))
28.3b
(/ (- (* b c) (* a 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
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
4.0ms
(+ (* c c) (* d d))
4.0ms
(- (* b c) (* a d))
9.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series47.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* c c) (* d d))
11.0ms
(- (* b c) (* a d))
30.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify975.0ms

Counts
64 → 64
Iterations

Useful iterations: done (973.0ms)

IterNodesCost
01011120
12891097
21143983
33674981
done5000980

prune126.0ms

Filtered
49 candidates to 64 candidates (-30.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New541064
Fresh000
Picked101
Done000
Total551065

Merged error: 28.0b

Counts
65 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b c) (* a d))
18.6b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.4b
(sqrt (+ (* c c) (* d d)))
29.4b
(sqrt (+ (* c c) (* d d)))

rewrite24.0ms

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
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
4.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (* b c) (* a d))
38.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms
(sqrt (+ (* c c) (* d d)))
6.0ms
(sqrt (+ (* c c) (* d d)))

simplify769.0ms

Counts
98 → 98
Iterations

Useful iterations: done (766.0ms)

IterNodesCost
01201814
13111691
29631577
329421558
done50001557

prune148.0ms

Filtered
78 candidates to 98 candidates (-25.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New93598
Fresh279
Picked101
Done000
Total9612108

Merged error: 24.7b

Counts
108 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
1.0b
(- (* b c) (* a d))
28.1b
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite33.0ms

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×div-exp add-log-exp
6×flip3-- flip-- div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×rec-exp frac-2neg flip3-+ 1-exp clear-num flip-+ associate-/l/
1×+-commutative sub-neg pow-flip diff-log sum-log inv-pow
Counts
4 → 138
Calls
4 calls:
4.0ms
(+ (* c c) (* d d))
10.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
4.0ms
(- (* b c) (* a d))
9.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* c c) (* d d))
30.0ms
(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
11.0ms
(- (* b c) (* a d))
24.0ms
(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify619.0ms

Counts
150 → 150
Iterations

Useful iterations: done (614.0ms)

IterNodesCost
02073684
15243488
219553196
done50003119

prune141.0ms

Filtered
88 candidates to 150 candidates (-70.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1482150
Fresh3811
Picked011
Done000
Total15111162

Merged error: 24.7b

Counts
162 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b c) (* d a))
18.6b
(/ (sqrt (+ (* d d) (* c c))) (- (* b c) (* d a)))
29.4b
(sqrt (+ (* d d) (* c c)))
29.4b
(sqrt (+ (* d d) (* c c)))

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 add-cbrt-cube associate-/l* add-log-exp
3×flip3-+ associate-/r* flip-+
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 85
Calls
4 calls:
4.0ms
(- (* b c) (* d a))
13.0ms
(/ (sqrt (+ (* d d) (* c c))) (- (* b c) (* d a)))
4.0ms
(sqrt (+ (* d d) (* c c)))
4.0ms
(sqrt (+ (* d d) (* c c)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (* b c) (* d a))
26.0ms
(/ (sqrt (+ (* d d) (* c c))) (- (* b c) (* d a)))
7.0ms
(sqrt (+ (* d d) (* c c)))
6.0ms
(sqrt (+ (* d d) (* c c)))

simplify607.0ms

Counts
97 → 97
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
01131782
12651665
27621565
320211548
done50001547

prune98.0ms

Filtered
73 candidates to 97 candidates (-32.9%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh099
Picked011
Done011
Total9612108

Merged error: 24.7b

Counts
108 → 12

regimes357.0ms

Accuracy

-11.7% (3.7b remaining)

Error of 27.1b against oracle of 23.3b and baseline of 26.7b

bsearch25.0ms

Steps
ItersRangePoint
9
-1.3189260295586262e+29
-2.5920945801387674e+23
-1.3042646303164026e+29

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02034
12834
23134
33434
done3434

end0.0ms

sample825.0ms

Algorithm
intervals
Results
412.0ms8461×body80valid

Profiling

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