Details

Time bar (total: 15.0s)

sample55.0ms

Algorithm
intervals
Results
19.0ms282×body80valid
5.0ms82×body80nan

simplify60.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
6.4b
(* (* x y) z)
7.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite105.0ms

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:
17.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) z)
36.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms
(sqrt (- (* z z) (* t a)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* z z) (* t a))
44.0ms
(* (* x y) z)
129.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
76.0ms
(sqrt (- (* z z) (* t a)))

simplify797.0ms

Counts
88 → 88

prune466.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
3.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite133.0ms

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:
28.0ms
(/ z (sqrt (- (* z z) (* t a))))
21.0ms
(- (* z z) (* t a))
60.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
16.0ms
(sqrt (- (* z z) (* t a)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ z (sqrt (- (* z z) (* t a))))
38.0ms
(- (* z z) (* t a))
120.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
122.0ms
(sqrt (- (* z z) (* t a)))

simplify979.0ms

Counts
124 → 124

prune498.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
1.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.9b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite165.0ms

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:
8.0ms
(- (* z z) (* t a))
63.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
74.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
16.0ms
(sqrt (- (* z z) (* t a)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* z z) (* t a))
88.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
157.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
106.0ms
(sqrt (- (* z z) (* t a)))

simplify923.0ms

Counts
104 → 104

prune425.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
3.8b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite74.0ms

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:
18.0ms
(/ (sqrt (- (* z z) (* t a))) z)
14.0ms
(- (* z z) (* t a))
23.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
13.0ms
(sqrt (- (* z z) (* t a)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (sqrt (- (* z z) (* t a))) z)
56.0ms
(- (* z z) (* t a))
162.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
103.0ms
(sqrt (- (* z z) (* t a)))

simplify985.0ms

Counts
144 → 144

prune627.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.6b

regimes585.0ms

Accuracy

80.7% (3.9b remaining)

Error of 7.6b against oracle of 3.6b and baseline of 24.1b

bsearch131.0ms

Steps
ItersRangePoint
6
9.556550840884058e+96
3.876059524135952e+97
1.1843780546868373e+97
9
-4.1007679679789613e+93
-9.34151210368374e+86
-1.8560343845112075e+93

simplify4.3s

end0.0ms

sample2.1s

Algorithm
intervals
Results
945.0ms8816×body80valid
194.0ms2941×body80nan