Details

Time bar (total: 9.4s)

sample21.0ms

Algorithm
intervals
Results
9.0ms269×body80valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57015
done7015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (* b c) (* a d))
27.7b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
8.0ms
(- (* b c) (* a d))
26.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series135.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(- (* b c) (* a d))
94.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.6s

Counts
50 → 50
Iterations

Useful iterations: 3 (462.0ms)

IterNodesCost
088954
1252936
2857854
32867850
done5000850

prune144.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 27.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b c) (* a d))
17.4b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
32.6b
(sqrt (+ (* c c) (* d d)))
32.6b
(sqrt (+ (* c c) (* d d)))

rewrite52.0ms

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:
7.0ms
(- (* b c) (* a d))
25.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
10.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(sqrt (+ (* c c) (* d d)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b c) (* a d))
118.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
36.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.4s

Counts
98 → 98
Iterations

Useful iterations: 3 (430.0ms)

IterNodesCost
01201814
13061682
28881574
325471558
done50001558

prune280.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 24.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b c) (* a d))
17.4b
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
32.6b
(sqrt (+ (* c c) (* d d)))
32.6b
(sqrt (+ (* c c) (* d d)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×sqrt-div add-log-exp
5×unswap-sqr
4×prod-exp
3×flip3-- flip3-+ associate-*l* flip-- flip-+
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv sub-neg rec-exp diff-log 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
7.0ms
(- (* b c) (* a d))
55.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
7.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(sqrt (+ (* c c) (* d d)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b c) (* a d))
118.0ms
(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
35.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.7s

Counts
107 → 107
Iterations

Useful iterations: 3 (783.0ms)

IterNodesCost
01471896
13711651
210581483
338021467
done50001467

prune288.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
17.4b
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
32.6b
(sqrt (+ (* c c) (* d d)))
32.6b
(sqrt (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×add-cube-cbrt *-un-lft-identity
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
9×associate-/l*
8×div-exp
7×pow1
6×sqrt-div div-inv
5×flip3-- flip--
4×cbrt-undiv add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
27.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
22.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
7.0ms
(sqrt (+ (* c c) (* d d)))
7.0ms
(sqrt (+ (* c c) (* d d)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
81.0ms
(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
40.0ms
(sqrt (+ (* c c) (* d d)))
36.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts
205 → 205
Iterations

Useful iterations: 3 (726.0ms)

IterNodesCost
02435682
15565079
212494732
334744666
done50004666

prune383.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 24.7b

regimes199.0ms

Accuracy

40.3% (1.8b remaining)

Error of 25.0b against oracle of 23.2b and baseline of 26.3b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02485
13575
done3575

end0.0ms

sample567.0ms

Algorithm
intervals
Results
285.0ms8473×body80valid