Details

Time bar (total: 9.1s)

sample31.0ms

Algorithm
intervals
Results
11.0ms282×body80valid
4.0ms103×body80nan

simplify56.0ms

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: 25.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
2.9b
(* (* x y) z)
11.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b
(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:
3.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
88.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify674.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
01341237
13431135
21586975
done5001975

prune247.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.5b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
9.0ms
(/ z (sqrt (- (* z z) (* t a))))
2.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
37.0ms
(- (* z z) (* t a))
86.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify889.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (279.0ms)

IterNodesCost
01662031
14291847
216521643
done50001643

prune320.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
0.9b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
2.0ms
(- (* z z) (* t a))
18.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
87.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
61.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
104 → 104
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01611572
14011453
211831241
343431240
done50001240

prune269.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
4.1b
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
24.3b
(cbrt (- (* z z) (* t a)))
24.3b
(cbrt (- (* z z) (* t a)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
34×add-exp-log associate-*r* add-cbrt-cube
33×add-cube-cbrt *-un-lft-identity
22×sqrt-prod
17×cbrt-prod
16×associate-*l*
13×prod-exp cbrt-unprod
11×pow1
8×cbrt-undiv div-exp unswap-sqr
6×cbrt-div
5×associate-*r/
4×pow-prod-down add-log-exp
3×flip3-- flip--
2×frac-times pow1/3 sqrt-div associate-*l/ associate-/r/ *-commutative div-inv
Counts
4 → 127
Calls
4 calls:
27.0ms
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
30.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms
(cbrt (- (* z z) (* t a)))
5.0ms
(cbrt (- (* z z) (* t a)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
146.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
87.0ms
(cbrt (- (* z z) (* t a)))
87.0ms
(cbrt (- (* z z) (* t a)))

simplify1.2s

Counts
139 → 139
Iterations

Useful iterations: 2 (622.0ms)

IterNodesCost
02613881
17443713
228953127
done50013127

prune454.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

regimes465.0ms

Accuracy

84.6% (2.9b remaining)

Error of 6.6b against oracle of 3.7b and baseline of 22.6b

bsearch105.0ms

Steps
ItersRangePoint
9
1.1514081473628363e+89
6.147715137559524e+97
8.840009572039548e+95
10
-2.167781788999652e+162
-1.4102566258715918e+152
-1.2137296334810365e+154

simplify5.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
02331
13231
24029
done4029

end0.0ms

sample827.0ms

Algorithm
intervals
Results
354.0ms8878×body80valid
102.0ms2953×body80nan