Details

Time bar (total: 8.4s)

sample21.0ms

Algorithm
intervals
Results
11.0ms264×body80valid

simplify34.0ms

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: 25.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
1.2b
(- (* b c) (* a d))
25.0b
(/ (- (* 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:
2.0ms
(+ (* c c) (* d d))
2.0ms
(- (* b c) (* a d))
11.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series147.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
37.0ms
(- (* b c) (* a d))
84.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.5s

Counts
64 → 64
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01011120
12891097
21023981
33794981
done5000980

prune180.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b c) (* a d))
15.9b
(/ (- (* b c) (* a 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
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:
3.0ms
(- (* b c) (* a d))
11.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
5.0ms
(sqrt (+ (* c c) (* d d)))
4.0ms
(sqrt (+ (* c c) (* d d)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* b c) (* a d))
108.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
37.0ms
(sqrt (+ (* c c) (* d d)))
34.0ms
(sqrt (+ (* c c) (* d d)))

simplify957.0ms

Counts
98 → 98
Iterations

Useful iterations: done (954.0ms)

IterNodesCost
01201814
13041682
28541574
325011558
done50001557

prune283.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.0b

localize13.0ms

Local error

Found 4 expressions with local error:

14.2b
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
16.5b
(cbrt (- (* b c) (* a d)))
16.5b
(cbrt (- (* b c) (* a d)))
16.5b
(cbrt (- (* b c) (* a d)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
25×add-sqr-sqrt
24×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
19×cbrt-prod
16×add-exp-log frac-times
15×flip3-- flip--
12×associate-*l/
10×add-cbrt-cube
9×pow1
6×prod-exp cbrt-unprod
5×associate-*r/
4×add-log-exp
3×pow1/3 pow-prod-down unswap-sqr
2×cbrt-undiv div-exp associate-/r/
1×flip3-+ associate-*l* *-commutative flip-+ div-inv
Counts
4 → 102
Calls
4 calls:
51.0ms
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
2.0ms
(cbrt (- (* b c) (* a d)))
2.0ms
(cbrt (- (* b c) (* a d)))
2.0ms
(cbrt (- (* b c) (* a d)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
110.0ms
(cbrt (- (* b c) (* a d)))
109.0ms
(cbrt (- (* b c) (* a d)))
108.0ms
(cbrt (- (* b c) (* a d)))

simplify942.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (291.0ms)

IterNodesCost
01973637
16033519
219642956
done50002956

prune386.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.0b

localize23.0ms

Local error

Found 4 expressions with local error:

16.5b
(cbrt (- (* b c) (* a d)))
21.6b
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
21.6b
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
21.6b
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
102×cbrt-prod
54×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-/r/
5×cbrt-div
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
3×flip3-+ flip-+ div-inv
1×flip3-- flip--
Counts
4 → 112
Calls
4 calls:
2.0ms
(cbrt (- (* b c) (* a d)))
5.0ms
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
5.0ms
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
5.0ms
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

series867.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(cbrt (- (* b c) (* a d)))
248.0ms
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
251.0ms
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
255.0ms
(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

simplify1.1s

Counts
124 → 124
Iterations

Useful iterations: 3 (460.0ms)

IterNodesCost
01963844
14333757
210703593
328363563
done50003563

prune523.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 23.0b

regimes195.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01325
11625
done1625

end0.0ms

sample469.0ms

Algorithm
intervals
Results
274.0ms8495×body80valid