Details

Time bar (total: 16.8s)

sample53.0ms

Algorithm
intervals
Results
17.0ms298×body80valid
6.0ms113×body80nan

simplify114.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36814
49314
511414
done11414

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.5b
(* (* x y) z)
9.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite116.0ms

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))
34.0ms
(* (* x y) z)
51.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms
(sqrt (- (* z z) (* t a)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) z)
130.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
107.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
88 → 88
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01341237
13691135
22350989
done5001987

prune429.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.7b
(* (* y z) x)
9.4b
(/ (pow (* (* y z) x) 1) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
26×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
21×add-exp-log sqrt-prod
11×add-cbrt-cube
10×pow1
7×unpow-prod-down sqr-pow
6×prod-exp associate-/r* add-log-exp
5×div-exp associate-/l*
4×sqrt-div
3×flip3-- associate-*r* pow-prod-down pow-exp flip-- cbrt-unprod
2×associate-/r/
1×cbrt-undiv pow-to-exp sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv
Counts
4 → 104
Calls
4 calls:
14.0ms
(- (* z z) (* t a))
28.0ms
(* (* y z) x)
28.0ms
(/ (pow (* (* y z) x) 1) (sqrt (- (* z z) (* t a))))
10.0ms
(sqrt (- (* z z) (* t a)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* z z) (* t a))
26.0ms
(* (* y z) x)
141.0ms
(/ (pow (* (* y z) x) 1) (sqrt (- (* z z) (* t a))))
117.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
116 → 116
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01822221
14141887
222561762
done50001758

prune516.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize45.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ (* (* z y) x) (sqrt (sqrt (- (* z z) (* t a))))))
5.5b
(/ (* (* z y) x) (sqrt (sqrt (- (* z z) (* t a)))))
24.9b
(sqrt (- (* z z) (* t a)))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
66×sqrt-prod
54×add-sqr-sqrt
51×times-frac
45×add-cbrt-cube
38×*-un-lft-identity
35×add-cube-cbrt
33×associate-*l*
31×prod-exp
23×div-exp
17×cbrt-unprod
16×sqrt-div
15×associate-*r*
13×cbrt-undiv
9×associate-/r*
8×pow1
7×unswap-sqr
6×associate-/r/
5×flip3-- flip--
4×rec-exp 1-exp add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 158
Calls
4 calls:
184.0ms
(* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ (* (* z y) x) (sqrt (sqrt (- (* z z) (* t a))))))
48.0ms
(/ (* (* z y) x) (sqrt (sqrt (- (* z z) (* t a)))))
10.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ (* (* z y) x) (sqrt (sqrt (- (* z z) (* t a))))))
136.0ms
(/ (* (* z y) x) (sqrt (sqrt (- (* z z) (* t a)))))
90.0ms
(sqrt (- (* z z) (* t a)))
103.0ms
(sqrt (- (* z z) (* t a)))

simplify4.4s

Counts
170 → 170
Iterations

Useful iterations: 2 (971.0ms)

IterNodesCost
02354622
17404233
247333590
done50003590

prune605.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

localize39.0ms

Local error

Found 4 expressions with local error:

24.9b
(sqrt (- (* z z) (* t a)))
24.9b
(sqrt (- (* z z) (* t a)))
24.9b
(sqrt (- (* z z) (* t a)))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

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 flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
10.0ms
(sqrt (- (* z z) (* t a)))
10.0ms
(sqrt (- (* z z) (* t a)))
12.0ms
(sqrt (- (* z z) (* t a)))
17.0ms
(sqrt (- (* z z) (* t a)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (- (* z z) (* t a)))
100.0ms
(sqrt (- (* z z) (* t a)))
71.0ms
(sqrt (- (* z z) (* t a)))
74.0ms
(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (737.0ms)

IterNodesCost
050956
1130848
2482776
32548772
done5001772

prune387.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.5b

regimes407.0ms

Accuracy

78.9% (4.5b remaining)

Error of 7.9b against oracle of 3.4b and baseline of 24.9b

bsearch140.0ms

Steps
ItersRangePoint
11
6.8410550143029e-38
1.3113650301339767e-12
1.292716185531284e-12
9
-3.113286269135709e+96
-3.4065764254652804e+90
-3.603369414995161e+90

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02231
13229
23429
done3429

end0.0ms

sample1.9s

Algorithm
intervals
Results
624.0ms8874×body80valid
201.0ms2948×body80nan