Details

Time bar (total: 8.9s)

sample20.0ms

Algorithm
intervals
Results
9.0ms277×body80valid

simplify33.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.8b
(- (* b c) (* a d))
26.6b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

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:
3.0ms
(+ (* c c) (* d d))
2.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series156.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
42.0ms
(- (* b c) (* a d))
87.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.0s

Counts
64 → 64
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
01011120
12891097
21062981
34744981
done5000981

prune169.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b c) (* a d))
15.5b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))

rewrite23.0ms

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:
2.0ms
(- (* b c) (* a d))
11.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* b c) (* a d))
111.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
33.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts
98 → 98
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01201814
13041682
28731574
328181558
done50001557

prune282.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize14.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
585×sqrt-prod
567×times-frac
302×add-sqr-sqrt
299×add-cube-cbrt *-un-lft-identity
50×sqrt-div
33×associate-/l*
22×associate-/r/
14×flip3-+ flip-+
11×div-inv
9×add-exp-log associate-/r* add-cbrt-cube
7×pow1
4×add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
2×div-sub
1×frac-2neg clear-num associate-/l/
Counts
4 → 402
Calls
4 calls:
31.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))
33.0ms
(sqrt (+ (* c c) (* d d)))
39.0ms
(sqrt (+ (* c c) (* d d)))
34.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.0s

Counts
414 → 414
Iterations

Useful iterations: done (985.0ms)

IterNodesCost
043620421
1102318015
2251916855
done500116853

prune729.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

localize19.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))
29.7b
(sqrt (+ (* c c) (* d d)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series146.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* c c) (* d d)))
40.0ms
(sqrt (+ (* c c) (* d d)))
34.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
038852
191744
2207680
3463656
41051656
52857656
done5000656

prune297.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.1b

regimes145.0ms

Accuracy

-5.8% (3.1b remaining)

Error of 26.8b against oracle of 23.7b and baseline of 26.7b

bsearch49.0ms

Steps
ItersRangePoint
10
6.409730244873951e+265
3.5402997186520582e+277
2.966297851011323e+277

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01840
12340
done2340

end0.0ms

sample505.0ms

Algorithm
intervals
Results
293.0ms8494×body80valid