Details

Time bar (total: 9.5s)

sample34.0ms

Algorithm
intervals
Results
10.0ms281×body80valid
4.0ms120×body80nan

simplify65.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36714
49214
510714
done10714

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.6b
(* (* x y) z)
7.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
16.0ms
(* (* x y) z)
28.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
11.0ms
(sqrt (- (* z z) (* t a)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
92.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify963.0ms

Counts
88 → 88
Iterations

Useful iterations: done (960.0ms)

IterNodesCost
01341237
13411135
21495975
done5001974

prune237.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
4.2b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
16.0ms
(/ (sqrt (- (* z z) (* t a))) z)
8.0ms
(- (* z z) (* t a))
23.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
9.0ms
(sqrt (- (* z z) (* t a)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (sqrt (- (* z z) (* t a))) z)
35.0ms
(- (* z z) (* t a))
93.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
144 → 144
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02102654
15002421
216412221
done50002218

prune337.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt z)
1.9b
(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
23.9b
(sqrt (- (* z z) (* t a)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
523×times-frac
382×add-sqr-sqrt
249×sqrt-prod
203×add-cube-cbrt *-un-lft-identity
179×associate-*r*
99×cbrt-prod
58×add-exp-log
48×add-cbrt-cube
44×associate-*l*
40×unswap-sqr
27×cbrt-undiv div-exp
15×prod-exp cbrt-unprod
8×pow1 div-inv
4×sqrt-div add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip--
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 340
Calls
4 calls:
1.0ms
(cbrt z)
224.0ms
(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
9.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt z)
112.0ms
(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
64.0ms
(sqrt (- (* z z) (* t a)))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify949.0ms

Counts
352 → 352
Iterations

Useful iterations: done (937.0ms)

IterNodesCost
057613190
1183712216
done500111391

prune947.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.0b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 227
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
18.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
51.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms
(sqrt (- (* z z) (* t a)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
58.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
93.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts
239 → 239
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03304875
17824362
222914138
done50014135

prune543.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.2b

regimes327.0ms

Accuracy

84.6% (3.0b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 22.7b

bsearch92.0ms

Steps
ItersRangePoint
9
3.897635107664822e+95
3.2935197406763337e+100
3.938152743281577e+96
9
-6.208254577570641e+60
-2.497316010543444e+54
-1.0028371986688996e+60

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02547
13247
23447
done3447

end0.0ms

sample985.0ms

Algorithm
intervals
Results
349.0ms8879×body80valid
107.0ms2977×body80nan