Details

Time bar (total: 7.4s)

sample29.0ms

Algorithm
intervals
Results
10.0ms280×body80valid
3.0ms93×body80nan

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12114
24414
36514
48914
510214
done10214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite26.0ms

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:
2.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
85.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify587.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
01341237
13501139
21756975
done5001975

prune237.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
2.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (sqrt (- (* z z) (* t a))) z)
32.0ms
(- (* z z) (* t a))
82.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify759.0ms

Counts
144 → 144
Iterations

Useful iterations: 2 (168.0ms)

IterNodesCost
02102654
15332433
223072221
done50002221

prune370.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.0b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.0b
(- (* z z) (* t a))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite63.0ms

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:
9.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
36.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
3.0ms
(- (* z z) (* t a))
4.0ms
(sqrt (- (* z z) (* t a)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
85.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
34.0ms
(- (* z z) (* t a))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
239 → 239
Iterations

Useful iterations: 2 (303.0ms)

IterNodesCost
03304875
18274402
235794138
done50004138

prune595.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (* x y) (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
10.4b
(/ (/ (* x y) (sqrt (- (* z z) (* t a)))) (/ 1 z))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
363×times-frac
143×add-sqr-sqrt
142×add-cube-cbrt *-un-lft-identity
51×sqrt-prod
48×add-exp-log
32×sqrt-div
31×associate-/r/
30×add-cbrt-cube
29×div-inv
28×div-exp
19×associate-/r*
17×flip3-- flip--
15×cbrt-undiv
13×associate-/l*
6×add-log-exp
5×pow1 prod-exp
3×rec-exp 1-exp cbrt-unprod
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 267
Calls
4 calls:
7.0ms
(/ (* x y) (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
18.0ms
(/ (/ (* x y) (sqrt (- (* z z) (* t a)))) (/ 1 z))
4.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (* x y) (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
82.0ms
(/ (/ (* x y) (sqrt (- (* z z) (* t a)))) (/ 1 z))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify453.0ms

Counts
279 → 279
Iterations

Useful iterations: done (444.0ms)

IterNodesCost
04327796
113406953
done50006275

prune483.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.3b

regimes407.0ms

Accuracy

84.7% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 22.3b

bsearch80.0ms

Steps
ItersRangePoint
7
4.43464859477407e+147
1.5123157394476474e+149
6.926066888201142e+147
9
-2.7283838574175814e+156
-2.1161453073457986e+149
-8.618354790122042e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12729
22929
done2929

end0.0ms

sample790.0ms

Algorithm
intervals
Results
339.0ms8864×body80valid
98.0ms2952×body80nan