Details

Time bar (total: 9.0s)

sample28.0ms

Algorithm
intervals
Results
10.0ms279×body80valid
3.0ms99×body80nan

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12114
24414
36514
48914
510214
done10214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
4.7b
(* (* x y) z)
8.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.4b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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))
6.0ms
(* (* x y) z)
13.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series200.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
28.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify816.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
01341237
13431139
21603975
done5000975

prune253.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
2.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.4b
(sqrt (- (* z z) (* t a)))

rewrite39.0ms

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:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
22.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
37.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
124 → 124
Iterations

Useful iterations: 2 (282.0ms)

IterNodesCost
01662031
14291861
217001647
done50011647

prune311.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

1.1b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.2b
(- (* z z) (* t a))
1.9b
(* y (/ z (sqrt (- (* z z) (* t a)))))
27.4b
(sqrt (- (* z z) (* t a)))

rewrite51.0ms

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:
22.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
3.0ms
(- (* z z) (* t a))
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
32.0ms
(- (* z z) (* t a))
56.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
104 → 104
Iterations

Useful iterations: 3 (909.0ms)

IterNodesCost
01611572
14011459
211981241
343551240
done50001240

prune254.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
7.2b
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
28.3b
(cbrt (- (* z z) (* t a)))
28.3b
(cbrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×times-frac
33×associate-*r*
32×add-cube-cbrt *-un-lft-identity
22×sqrt-prod
17×cbrt-prod
16×add-exp-log add-cbrt-cube
13×associate-*l*
8×unswap-sqr
6×pow1 cbrt-div add-log-exp
4×cbrt-undiv flip3-- div-exp prod-exp flip-- cbrt-unprod
2×pow1/3 sqrt-div associate-/r/ div-inv
1×frac-times sub-neg diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 112
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
35.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* z z) (* t a))
147.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
88.0ms
(cbrt (- (* z z) (* t a)))
84.0ms
(cbrt (- (* z z) (* t a)))

simplify1.2s

Counts
124 → 124
Iterations

Useful iterations: 2 (427.0ms)

IterNodesCost
02343022
16472905
222302559
done50002559

prune453.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

regimes336.0ms

Accuracy

83.4% (3.1b remaining)

Error of 7.3b against oracle of 4.2b and baseline of 22.8b

bsearch92.0ms

Steps
ItersRangePoint
5
2.630451539791177e+79
8.765004478552205e+79
2.9066318437014138e+79
9
-5.265129340759454e+73
-8.378710405837631e+67
-2.973010024434297e+73

simplify7.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
03446
14144
24243
35343
done5343

end0.0ms

sample783.0ms

Algorithm
intervals
Results
339.0ms8834×body80valid
97.0ms2913×body80nan